Math1.2- Unit 9 Material

Relation

Any set of ordered pairs $(x, y)$.

Function

A relation where each input ($x$) has exactly one output ($y$).

Domain

The set of all possible input values ($x$).

Range

The set of all possible output values ($y$).

Vertical Line Test (VLT)

A test used on a graph to determine if it is a function; if a vertical line touches more than one point, it is NOT a function.

Evaluating $f(x)$

Replacing the variable $x$ with a given value and solving the equation.

Evaluating $f(1)$ for $f(x) = 2x - 3$

$f(1) = 2(1) - 3 = -1$.

Evaluating $g(-2)$ for $g(x) = x^{2} - 2x$

$g(-2) = (-2)^{2} - 2(-2) = 4 + 4 = 8$.

Domain Red Flag: Fractions

The denominator of a fraction cannot be zero.

Domain Red Flag: Square Roots

The expression under a square root must be greater than or equal to zero.

Domain of $f(x) = \frac{1}{x-4}$

All real numbers except $x = 4$.

Domain of $f(x) = \sqrt{x+2}$

$x \ge -2$ (or $[-2, \infty)$).

Relative Maximum

A "peak" or high point on a graph where the function changes from increasing to decreasing.

Relative Minimum

A "valley" or low point on a graph where the function changes from decreasing to increasing.

Increasing Function

A function is increasing on an interval if the graph goes "up" from left to right.

Decreasing Function

A function is decreasing on an interval if the graph goes "down" from left to right.

Constant Function

A function is constant on an interval if the graph is a flat horizontal line.